Krichoff’S Law - Finding Internal Resistance Of Battery

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Topic: Kirchhoff’s Law - Finding Internal Resistance of Battery
Introduction to Kirchhoff’s Laws
Overview of Internal Resistance
Importance of finding Internal Resistance

Slide 2

Kirchhoff’s Laws
Explanation of Kirchhoff’s Current Law (KCL)
Explanation of Kirchhoff’s Voltage Law (KVL)
Importance of Kirchhoff’s Laws in analyzing circuits

Slide 3

Internal Resistance of a Battery
Definition of Internal Resistance
How does Internal Resistance affect the battery performance?
Importance of measuring Internal Resistance

Slide 4

Experimental Setup for measuring Internal Resistance
Circuit diagram with a cell, ammeter, voltmeter, and adjustable resistor
Procedure for measuring Internal Resistance
Calculation of Internal Resistance using Kirchhoff’s Laws

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Using KVL to analyze a circuit with Internal Resistance
Example circuit diagram
Voltage drops across different components
Formulating equations using KVL

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Using KCL to analyze a circuit with Internal Resistance
Example circuit diagram
Current flow through different branches
Formulating equations using KCL

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Combining KVL and KCL to solve circuits with Internal Resistance
Example circuit diagram
Steps to solve the circuit using both laws simultaneously
Solving for the unknown variables

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Calculating the Internal Resistance from Experimental Data
Example experimental data table
Voltage and Current measurements
Plotting a graph and determining the slope

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Importance of accurate measurement of Internal Resistance
Impact of Internal Resistance on circuit performance
Effects on battery life and efficiency
Applications in real-life circuits

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Recap and Key Points
Summary of Kirchhoff’s Laws
Understanding Internal Resistance and its significance
Importance of measuring Internal Resistance accurately

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Determining the E.m.f. and Internal Resistance of a Battery
Equation for the terminal potential difference of a cell: V = E - Ir where V is the terminal potential difference, E is the electromotive force (E.m.f.) of the cell, I is the current flowing through the circuit, and r is the internal resistance of the battery.
Rearranging the equation: r = (E - V)/I This equation allows us to calculate the internal resistance of a battery using experimental data.
Example: If a battery has an E.m.f. of 12V and a terminal potential difference of 10V with a current of 2A, then the internal resistance can be calculated as: r = (12V - 10V)/2A = 1Ω

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Factors affecting the Internal Resistance of a Battery
Temperature: Increase in temperature typically leads to an increase in internal resistance.
Age and condition of the battery: Older or damaged batteries tend to have higher internal resistance.
Chemistry of the battery: The type of battery and chemical reactions inside can impact its internal resistance.
Example: A brand new alkaline battery may have an internal resistance of 0.1Ω, while an old and deteriorated battery may have an internal resistance of 1Ω or more.

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Significance of Internal Resistance in circuit analysis
Voltage drops: Internal resistance causes a voltage drop within the battery, reducing the terminal potential difference available for the external circuit.
Power dissipation: Internal resistance leads to power dissipation within the battery, causing it to get warm during use.
Effect on current flow: Internal resistance limits the maximum current that can be drawn from the battery.
Example: In a circuit with a nominal voltage requirement of 9V and a battery with an internal resistance of 1Ω, the available voltage for the circuit would be reduced to 8V due to the voltage drop across the internal resistance.

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Equivalence of a Real Battery to an Ideal Battery and a Resistor
An ideal battery can be represented as an ideal voltage source with no internal resistance.
A real battery can be represented as an ideal voltage source in series with an internal resistor.
Equivalent circuit representation: Ideal battery: Real battery: _____ _____
- | E | - + | E | - ¯¯¯¯¯ ¯¯¯¯¯
  | R_internal |

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Application of Internal Resistance - Voltage Regulation in Circuits
The presence of internal resistance affects the output voltage stability of a battery-powered circuit.
Voltage regulation is the ability of a circuit to maintain a relatively constant output voltage even as the load resistance changes.
Example: A voltage regulator circuit can be designed to compensate for the voltage drop caused by the internal resistance of a battery, ensuring a stable output voltage for the circuit regardless of the load resistance.

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Internal Resistance and Battery Efficiency
Battery efficiency can be affected by its internal resistance.
The power efficiency of a battery is given by: η = (load resistance / (load resistance + internal resistance)) * 100% where η is the efficiency, load resistance is the external resistance connected to the battery, and internal resistance is the internal resistance of the battery.
Example: If a battery has an internal resistance of 2Ω and a load resistance of 10Ω, the battery efficiency would be: η = (10Ω / (10Ω + 2Ω)) * 100% = 83.33%

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Effect of Low and High Internal Resistance
Low internal resistance benefits circuits that require high currents, as it allows a greater amount of current to flow.
High internal resistance is undesirable as it leads to significant voltage drops and reduced power delivered to the circuit.
Example: In an electric vehicle with a powerful motor, a battery with low internal resistance is preferred to supply the high current required for efficient operation.

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Factors Affecting the Accuracy of Internal Resistance Measurement
Measurement instruments: The accuracy and precision of ammeters, voltmeters, and other measurement tools impact the accuracy of the calculated internal resistance.
Contact resistance: Poor connections between the battery terminals and measurement instruments can introduce additional resistance.
Battery state: Age, condition, and charge level of the battery can affect internal resistance measurement accuracy.
Example: To minimize measurement inaccuracies, high-quality measurement instruments and secure connections should be used, and batteries should be in good condition.

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Importance of Internal Resistance in Battery Selection
Understanding the internal resistance of a battery is crucial for selecting the appropriate battery for the desired application.
Certain applications require batteries with low internal resistance to meet the high power demands, while others may benefit from higher internal resistance to prevent excessive current flow.
Example: In applications like power tools or electric vehicles, batteries with low internal resistance are preferred, while in low-power devices with long battery life requirements, batteries with a higher internal resistance can be more suitable.

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Conclusion and Recap
Kirchhoff’s Laws play a vital role in analyzing circuits with internal resistance.
Internal resistance affects the performance and efficiency of batteries.
Terminal potential difference can be used to calculate internal resistance.
Internal resistance impacts voltage drops, power dissipation, and current flow in a circuit.
Understanding internal resistance aids in battery selection and voltage regulation.
Accurate measurement and consideration of factors affecting internal resistance are essential.

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Application of Internal Resistance in Circuits
- Voltage dividers: Internal resistance can be utilized to create voltage dividers, which are commonly used in electronic circuits to obtain a desired voltage from a higher voltage source.
- Current limiting: The internal resistance of a battery can act as a current-limiting device in a circuit by reducing the maximum current that can flow through the circuit.
- Temperature monitoring: Changes in the internal resistance of a battery with temperature can be utilized for temperature monitoring in certain applications.

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Calculating Internal Resistance - Example 1
- Given:
  - Battery E.m.f. (E) = 10V
  - Terminal potential difference (V) = 8V
  - Current (I) = 2A
- Calculation:
  - Internal resistance (r) = (E - V) / I = (10V - 8V) / 2A = 2V / 2A = 1Ω
- The internal resistance of the battery is calculated to be 1Ω.

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Calculating Internal Resistance - Example 2
- Given:
  - Battery E.m.f. (E) = 15V
  - Terminal potential difference (V) = 13V
  - Current (I) = 3A
- Calculation:
  - Internal resistance (r) = (E - V) / I = (15V - 13V) / 3A = 2V / 3A = 0.67Ω
- The internal resistance of the battery is calculated to be approximately 0.67Ω.

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Terminal Potential Difference - Example 1
- Given:
  - Battery E.m.f. (E) = 12V
  - Internal resistance (r) = 1Ω
  - Current (I) = 4A
- Calculation:
  - Terminal potential difference (V) = E - (I * r) = 12V - (4A * 1Ω) = 12V - 4V = 8V
- The terminal potential difference of the battery is calculated to be 8V.

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Terminal Potential Difference - Example 2
- Given:
  - Battery E.m.f. (E) = 20V
  - Internal resistance (r) = 2Ω
  - Current (I) = 5A
- Calculation:
  - Terminal potential difference (V) = E - (I * r) = 20V - (5A * 2Ω) = 20V - 10V = 10V
- The terminal potential difference of the battery is calculated to be 10V.

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Voltage Drop Across Internal Resistance - Example 1
- Given:
  - Battery E.m.f. (E) = 9V
  - Internal resistance (r) = 0.5Ω
  - Current (I) = 3A
- Calculation:
  - Voltage drop across internal resistance = I * r = 3A * 0.5Ω = 1.5V
- The voltage drop across the internal resistance is calculated to be 1.5V.

Slide 27

Voltage Drop Across Internal Resistance - Example 2
- Given:
  - Battery E.m.f. (E) = 24V
  - Internal resistance (r) = 2.5Ω
  - Current (I) = 2A
- Calculation:
  - Voltage drop across internal resistance = I * r = 2A * 2.5Ω = 5V
- The voltage drop across the internal resistance is calculated to be 5V.

Slide 28

Power Dissipation in Internal Resistance - Example 1
- Given:
  - Battery E.m.f. (E) = 15V
  - Internal resistance (r) = 1Ω
  - Current (I) = 5A
- Calculation:
  - Power dissipation in internal resistance = (I^2) * r = (5A)^2 * 1Ω = 25W
- The power dissipation in the internal resistance is calculated to be 25W.

Slide 29

Power Dissipation in Internal Resistance - Example 2
- Given:
  - Battery E.m.f. (E) = 12V
  - Internal resistance (r) = 2Ω
  - Current (I) = 3A
- Calculation:
  - Power dissipation in internal resistance = (I^2) * r = (3A)^2 * 2Ω = 18W
- The power dissipation in the internal resistance is calculated to be 18W.

Slide 30

Recap and Key Points
- Kirchhoff’s Laws are essential for analyzing circuits with internal resistance.
- Internal resistance affects voltage drops, power dissipation, and current flow in a circuit.
- Internal resistance can be calculated using the terminal potential difference and current.
- Voltage dividers and current limiting are practical applications of internal resistance.
- Battery efficiency and voltage regulation depend on internal resistance.
- Accurate measurement and consideration of factors affecting internal resistance are crucial for proper circuit analysis.